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On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy
Comptes Rendus. Mathématique, Tome 359 (2021) no. 3, pp. 249-256.

Dans cette note nous nous intéressons à l’analyse de stabilité de la méthode de couches absorbantes parfaitement adaptées (PMLs) pour la propagation d’ondes électromagnétiques en régime transitoire dans un milieu anisotrope décrit par un tenseur diélectrique diagonal. Contrairement aux cas de l’équation d’ondes scalaire 3D et des équations de Maxwell 2D, certaines anisotropies diagonales mènent à l’existence d’ondes inverses qui provoquent des instabilités de la méthode PML. Ce résultat est illustré par des simulations numériques.

The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell’s equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.

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DOI : https://doi.org/10.5802/crmath.165
Éliane Bécache 1 ; Sonia Fliss 1 ; Maryna Kachanovska 1 ; Maria Kazakova 2

1. Labratoire POEMS, CNRS, Inria, ENSTA Paris Institut Polytechnique de Paris, 828 boulevard des Maréchaux, 91762 Palaiseau, France
2. Normandie Univ, INSA de Rouen Normandie, LMI (EA 3226 - FR CNRS 3335), 76000 Rouen, France, 685 Avenue de l’Université, 76801 St Etienne du Rouvray cedex, France
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     title = {On a surprising instability result of {Perfectly} {Matched} {Layers} for {Maxwell{\textquoteright}s} equations in {3D} media with diagonal anisotropy},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {249--256},
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     volume = {359},
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Éliane Bécache; Sonia Fliss; Maryna Kachanovska; Maria Kazakova. On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy. Comptes Rendus. Mathématique, Tome 359 (2021) no. 3, pp. 249-256. doi : 10.5802/crmath.165. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.165/

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